Question

In an equilateral triangle of side is a ,find the length of the altitude

Answer 1

Answer:

$\frac{a}{ \sqrt{2} }$

Step-by-step explanation:

In an equilateral ∆ , all sides are equal

so, each side = a

draw a perpendicular from one vertex to the opposite side in such a way that it bisects the side...

that is a/2

consider the half ∆ ,

hypotenuse a

base a/2

Altitude^2 = Hypotenuse^2 - Base^2

= a^2 - (a/2)^2

= 2a^2 - a^2/2

=a^2/2

Altitude = √a^2/2

= a/√2